Bibliographic record
Abstract
This thesis is about constructions of canonical metrics in complex non-Kähler geome- try, focusing in particular on balanced metrics satisfying special hermitian curvature conditions. More specifically, we adapt gluing strategies from Kähler geometry to obtain families of balanced metrics with special curvature properties, with particular relevance for the constructions of solutions of the Hull-Strominger system and the geometrization of balanced classes. More specifically, we show that: crepant resolutions of orbifolds with isolated singularities admitting singular Chern-Ricci flat balanced metrics can also be endowed with Chern-Ricci flat balanced metrics; small resolutions of smoothable Calabi-Yau singular threefolds with a finite family of Ordinary Double Points admit an approximately Chern-Ricci flat balanced metric; the blowup at a finite family of points of a compact Chern-Ricci flat balanced manifold always admits Chern-scalar constant balanced metrics. In all three cases we have a control on the Bott-Chern cohomology class of metrics constructed. Furthermore, we use representation theory techniques to construct special balanced metrics on the class of real simple Lie groups of inner type, as well as on the corresponding compact homogeneous spaces, on which we obtain that the metrics constructed are Chern-scalar with non-vanishing Chern-Ricci tensor, providing a family of compact complex manifolds with vanishing first Chern class and non-vanishing first Bott-Chern class. Moreover, we show that for this class of homogeneous spaces the Fino-Vezzoni conjecture holds.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.000 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".